1)     in the diagram below, we have $\overline{QR}\parallel\overline{ST}$$PQ = 8$$QS = 6$, and $PT = 10.5$. Find $PR$.

[asy] size(5cm);pair P,Q,R,SS,T;P = (0,0);Q = (0.5,0.6);R = (0.6,0);SS = 1.75*Q;T = 1.75*R;draw (Q--R--T--SS--P--R);label(


2)    In the diagram below, we have $\overline{MN}\parallel\overline{PQ}$. We also know that $OM = 9$$OQ = 6$, and $PN = 25$. Find $OP$

[asy] size(5cm);pair O,M,NN,P,Q;M = (-0.3,0.5);NN = (0.6,0.5);P = -0.7*NN;Q = -0.7*M;label(





3)       In the diagram, angles $ABC$ and $ADE$ are right angles. If $AC = 35$$AE = 11$, and $BE = 10$, then what is $AD$?

[asy] pair A,B,C,D,EE;B = (0,0);A = (1,0);C = (0,0.7);EE = (0.4,0);D = foot(EE,A,C);draw(D--EE--A--C--B--E);draw(rightanglemark(A,B,C,1.5));draw(rightanglemark(EE,D,A,1.5));label(



4)        $E$ is a point on side $\overline{CD}$ of square $ABCD$ such that $DE=2$ and $EC=5.$ The extensions of $\overline {AD}$ and $\overline {BE}$ intersect at $F.$ Find $DF.$

[asy] size(5cm);pair A,B,C,D,EE,F;A=(0,0);B=(6,0);D=(0,6);C=B+D;EE=(C+2D)/3;F=3D/2;draw(B--C--D--F--B--A--D);label(




5)          In the diagram below, we have $\triangle MNO\sim\triangle NRO\sim\triangle QPO.$ What is $\angle MNR$ in degrees?

[asy] pair O,M,NN,P,Q,R;M = (-0.4,0.5);R=0.75M;NN = (0.3,0.5);P = -0.9*NN;Q = -0.9*M;label(




6)       Segments $\overline{AC}$ and $\overline{BD}$ intersect at $O$. We know that $\dfrac{OA}{OB}=\dfrac{OD}{OC}$. Which angles below are equal to $\angle CDB$?

(w) $\angle ADB$
(x) $\angle CAB$
(y) $\angle BCA$
(z) $\angle ABD+\angle ACD$
[asy] size(5cm);pair A,B,C,D,O;A = 2*dir(15);B = 4*dir(140);C = -3A;D = -0.75B;draw(A--B--C--D--A--C^^B--D);label(

Guest Oct 27, 2017

you do not have to explain how you do it so if you want to give just the answer you can   smiley

Guest Oct 28, 2017

12 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.